What is simplest way to join particles into a single mesh and modify during animation?
A single mesh can be created from a particle system by using modifiers.


Create a particle system. For this example, also create a container to keep the particles in a volume.
Add a cube which fully encloses the particle system and its container. After some simulation, the geometry will look like this:





Add a sphere which will be used to display the particle system. Any manifold object can be used. If non-manifold objects are used, this solution will not work.
Add a modifier to make this sphere a particle system instance. At this point, each sphere is a separate mesh. Therefore, filtering modifiers operate on each sphere, not the combined mesh. 


 



Add a modifier to perform an intersection with the particle system and the largest cube. This will create a single mesh from all of the spheres.
Add a Laplacian Smooth modifier. The mesh will be smoothed eliminating the appearance of intersecting spheres.


 



Now other operations like Booleans can be applied.